We are flying in to Madrid Airport and immediately traveling to Seville. What is the best means of transportation to get there and most economical? Many Thanks!
Bus - http://www.socibus.es/index.jsp Train - http://www.renfe.com/ Thoughts - What do you want from 'best', apart from economical? You do not say when, so either flight, train, bus or rental car might be feasible depending on this 'best'.
How quick do you want to arrive in Seville, will you be time wealthy enough for a six odd hours busjourney, if money does matter? Sure you want to do this immediately after a (presumably) transatlantic flight?
The simplest and probably the easiest is to take the bus from the airport to the train station and grab the first train to Seville. You could get a discount for pre-purchasing your ticket but that carries some risk if your plane is late or delayed. The train station is decent and if you have some extra time you can grab lunch or breakfast.
The airport bus to Atocha station is cheap (2 euro) easy and very comfortable. You can save 100 euros on 2 tickets on the AVE (train) from Madrid to Sevilla by booking in advance, but as Frank said that is tricky timing after an overseas flight. So even though it is not the cheapest option, his suggestion to just head to Atocha and buy seats on the next train out is the fastest and the one I would choose. The train ride is only 2.5 hours and very comfortable.